find the equation of a straight line passing through the point (3,3) which is perpendicular to the line y=-1/2x-4

Answer:

x=-3y

Step-by-step explanation:

-2x-6y=0

x+3y=0

x=-3y

Answer:

Step-by-step explanation:

Summation means that you are adding together all the numbers that result from putting in the numbers 5-11 for i:

(-7 - 6(5)) + (-7 - 6(6)) + (-7 - 6(7)) + ( -7 - 6(8)) + ( -7 - 6(9)) + ( -7 - 6(10)) + ( -7 - 6(11)) which gives you the numbers:

-37 + -43 + -49 + -55 + -61 + -67 + -73 = -385

STEPS:

First distribute the 5 through the parentheses to get 5q + 135. So the problem now reads 5q + 135 - (-30) = 95.

Now, minus a negative can be changed to plus a positive so - (-30) can be changed to +30 so our equation now reads 5q + 135 + 30 = 95.

Before adding or subtracting anything from both sides of the equation, make sure you simplify the left side as much as possible. Notice that we can add 135 and 30 to get 165 so the left side simplifies to 5q + 165 = 95.

Now we can simply subtract 165 from both sides of the equation to get 5q = -70.

Now simply divide both sides of the equation by 5 to get q = -14.

Answer: The numbers are 10 and 23

Step-by-step explanation:

Let the smaller number be x

And the larger number be y

Ist sentence;

1. The sum of two numbers is 33.

X + y= 33 .........eqn 1

2. second sentence

the larger number is 3 more than two times the smaller number.

Y = 3 +2x

Put y into eqn 1

X+ 3 +2x = 33

3x= 33- 3

3x= 30

X = 30/3

X= 10 and y= 3+ 2x

Y= 3+ 2(10)

Y = 3+ 20

Y= 23

Therefore the two numbers are 10 and 23

Answer:

1) up

2) correct

3) left

4) down

Step-by-step explanation:

do you not have a graphing calculator, it really helps you with these.

The parabola opens by matching an equation are as follows,

The standard equation of a regular parabola exists [tex]y^{2} = 4ax.[/tex] Some of the important representations below are helpful to understanding the features and parts of a parabola. Focus: The point (a, 0) is the focus of the parabola.

A parabola is a plane curve that exists mirror-symmetrical and is approximately U-shaped. It fits several superficially various mathematical descriptions, which can all be established to define the same curves.

The parabola opens by matching an equation are as follows,

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Answer:

The number of trucks and sedans can be

(0 trucks ,26 sedans)

(8 trucks ,21 sedans)

(24 trucks ,11 sedans)

(25 trucks ,1 sedans)

(32 trucks ,6 sedans)

(16 trucks ,16 sedans)

Step-by-step explanation:

Given:

The  cost for trucks =$5

The cost for sedans  =$8

The total amount collected = $208

To Find:

Number of trucks and sedans passed through the toll booth =?

Solution:

Let the number of trucks be x and the number of sedans be y

Then

5x + 8y = 208-------------------------------(1)

By Trail and error method

5(0) + 8(26) = 208

5(8) + 8(21) = 208

5(24) +8(11) =208

5(25) + 8(1) = 208

5(32) + 8(6) =208

5(16) + 8(16) = 208

Answer:

0

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-2-(-2))/(5-(-3))

m=(-2+2)/(5+3)

m=0/8

m=0

Answer:

Step-by-step explanation:

ΔABC ≅ ΔABD  by ASA

Answer:

Step-by-step explanation:

We need to find the option for which the value of the function will be increasing, with the increasing variable.

Vertical line means the value of the x is constant, for any y. Hence, it is not the answer.

Horizontal line represents constant functions. Hence option B can not be the answer.

The data having a positive slope represents a increasing function with the increasing variable. Vice-versa for the data having a negative slope.

That is why option D will be the answer.

The correct option is d, which is the data canvas be modeled by a line with a negative slope.

A scatter plot is also known as a scatter chart, a scatter graph that uses dots to represent values for two different numeric variables. Each dot on the graph represents a particular on both the axis.

the Y values are decreasing as the x-values are increasing

As we can see in the graph below with the decreasing value of y and increasing value of x, therefore, it will be a negative slope.

Hence, the correct option is d, which is the data canvas be modeled by a line with a negative slope.

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Answer:

m = -1/2

Step-by-step explanation:

As we move from the point (-1, 7) to the point (3, 5), x increases by 4 (this is the "run") and y decreases by 2 (this is the "rise").

Thus, the slope of the line connecting these two points is

m = rise / run = -2/4, or m = -1/2.

Answer:

1/2

Step-by-step explanation:

Answer:

Matt bought 7 packages of hot dogs and 5 packages of hamburger.

Step-by-step explanation:

We are given the following in the question

Let x represent the number of packages of hot dogs.

Cost of one packet of hot dog = $2.75

Let y represent the number of packages of hamburgers

Cost of one packet of hamburgers = $3.20

Then, we can write the following equations:

[tex]x + y = 12\\2.75x + 3.2y = 35.25[/tex]

Solving the two equations,

[tex]2.75x + 2.75y = 33\\2.75x + 3.2y = 35.25\\\Rightarrow 0.45y = 2.25\\y = 5\\x = 7[/tex]

Thus, Matt bought 7 packages of hot dogs and 5 packages of hamburger.

The solution is viable.

Constraints to the system of equation:

[tex]x,y \geq 0 \\x + y = 12\\2.75x + 3.2y = 35.25[/tex]

Answer:

Step-by-step explanation:

Complete the square to do this.  This one is a bit of a pain because of the 7 as our linear term, but a little hard work never killed anyone!

The rules for completing the square are very strict and cannot be strayed from.  The first rule is that the leading coefficient HAS to be a positive 1; ours is a positive 6 so we have to factor it out.  Let's do that first then we can get to rule number 2.

Set the quadratic equal to 0, then move the constant over to the other side.  This is not a rule, per se, but I teach it this way to avoid unnecessary confusion in an already confusing process.  

[tex]6x^2+7x=-2[/tex] and to factor out the 6:

[tex]6(x^2+\frac{7}{6}x)=-2[/tex]

Now for rule #2:  take half the linear term, square it, and add it to both sides.  Our linear term is 7/6.  Half of that is 7/12, and 7/12 squared is 49/144.  BUT we cannot forget about that 6 hanging around out front, refusing to be ignored.  It is a multiplier, so when we add 49/144 inside the parenthesis on the left, we have to add 6(49/144) to the right, giving us:

[tex]6(x^2+\frac{7}{6}x+\frac{49}{144})=-2+\frac{294}{144}[/tex]

We will rewrite now by simplifying.  The left side can be written into a perfect square binomial (which is why we did this in the first place) and the right side can be added.  The left side becomes

[tex]6(x+\frac{7}{12})^2[/tex]

The 7/12 comes from the square root of 49/144, and the x comes from the square root of x-squared.  The right side requires a common denominator:

[tex]-2+\frac{294}{144}=-\frac{288}{144}+\frac{294}{144}=\frac{6}{144}=\frac{1}{24}[/tex]

So now we have

[tex]6(x+\frac{7}{12})^2=\frac{1}{24}[/tex]

Put evertyhing back onto the left side and set it back to equal y and you're done!

[tex]y=6(x+\frac{7}{12})^2-\frac{1}{24}[/tex]

Because the vertex form of a quadratic does not allow us to stray from the format "x -", we have to interpret our h coordinate as "x - (-7/12))" which is movement to the left.  This gives us a vertex of

[tex](-\frac{7}{12},-\frac{1}{24})[/tex]

Answer:

f(g(x))=(x-2)^2 - 7

(x-2)(x-2) - 7

x^2-2x-2x+4-7

x^2-4x-3

g(f(x))=x^2-2-7

x^2-9

(x+3)(x-3)

Step-by-step explanation:

To evaluate functions, you substitute x with the given value in the function and perform the calculation. For example, evaluating f(3) for the function f(x)=x^2-7 gives f(3)=2, while evaluating g(3) for the function g(x)=x-2 gives g(3)=1.

The functions given are f(x)=x^2-7 and g(x)=x-2. To evaluate these functions, we substitute a value for x into the function and perform the calculation. For example, if we want to evaluate f(3), we replace x in the function f(x) with 3.

So for f(3)=3^2-7, we do the following: f(3)=9-7=2.

For g(3), we substitute x in the function g(x) with 3: g(3)=3-2=1

It's important to note that the value you're evaluating might change depending on the question, but this is the basic process for evaluating a function at a given value or values.

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Answer:

2 cups of sugar

Step-by-step explanation:

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

3x + 5 + 4x = 5x + 27

7x + 5 = 5x + 27

- 5

7x = 5x + 22

- 5x

2x = 22

/2

x = 11

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Answer:

Step-by-step explanation:

3x + 5 + 4x = 5x + 27

collect like terms

7x - 5x = 27 -5

2x = 22

divide both side by 2

x = 11

answer:C=10+10n

proof: 10+10 (1)=20

10+10 (.6)=16

10+10 (-.4)=6

Answer:

Step-by-step explanation:

The basic concept for both is the same, except with grouping you have more than 3 terms and after factoring out what is common in each group, you are left with identical terms in a set of parenthesis that can then also be factored out.  For example, this would be factoring by grouping (then I will show you a factoring by GCF to better illustrate the idea):

If our polynomial is

[tex]x^3-x^2+3x-3=0[/tex]

we could group those terms into groups of 2 (without changing their order at all) to get:

[tex](x^3-x^2)+(3x-3)=0[/tex]

and we factor out what's common in each group to get:

[tex]x^2(x-1)+3(x-1)=0[/tex]

You can see that the (x - 1) is common now and can be factored out, leaving us with

[tex](x-1)(x^2+3)[/tex] (the secod term now can be factored if you need the complete linear factorization, but it will lead to imaginary numbers).  

An example of factoring out the GCF is to factor out what's common in all the terms.  It HAS TO BE COMMON IN ALL THE TERMS to do it this way.  For example, in the polynomial

[tex]6x^3-4x^2+2x-8=0[/tex] the GCF for all the terms is a 2, so that's all we can factor out.  It has to factor out of every term every time, no exceptions:

[tex]2(3x^3-2x^2+x-4)=0[/tex]

The method of GCF factoring often just serves to simplify the polynomial down a bit, but sometimes will still require factoring.

Final answer:

Factoring by grouping is used for polynomials with four or more terms, arranging them into groups with common factors, while factoring by GCF involves finding the largest common factor for all terms in an expression.

Explanation:

Factoring by grouping and factoring by the Greatest Common Factor (GCF) are two methods used in algebra to simplify expressions or solve equations.

Factoring by GCF involves finding the largest factor that is common to all terms in an expression.

For example, in the expression 4x + 8, the GCF is 4, so we can factor it as 4(x + 2).

Factoring by grouping, on the other hand, is used when an expression has four or more terms.

The method involves grouping terms so that each group has a common factor that can be factored out.

For instance, with the polynomial x^3 + 3x^2 + 4x + 12, we group the terms into (x^3 + 3x^2) + (4x + 12).

We then factor out the GCF from each group, yielding x^2(x + 3) + 4(x + 3).

Recognizing that (x + 3) is common between the groups, we can then factor further to get (x^2 + 4)(x + 3).

Answer:

See the explanation

Step-by-step explanation:

Given function

[tex]Y=3x+1[/tex]

We need to find [tex]y[/tex] value corresponding to each [tex]x[/tex] value.

So, plug each [tex]x[/tex] value in equation we get,

[tex]plug\ x=4\\y=3(4)+1\\y=12+1\\y=13\\\\plug\ x=6\\y=3(6)+1\\y=18+1\\y=19\\\\plug\ x=10\\y=3(10)+1\\y=30+1\\y=31[/tex]

Now in next part of question it ask us to check each ordered pair.

Let us plug each [tex]x[/tex] value and [tex]y[/tex] value in the function [tex]y=-3x-5[/tex]

[tex]plug\ (1,-8)\\-8=-3(1)-5\\-8=-3-5\\-8=-8\\\\plug(-5,0)\\0=-3(-5)-5\\0=15-5\\0\neq10\\\\plug\ (-2,1)\\1=-3(-2)-5\\1=6-5\\1=1\\\\plug\ (-1,-2)\\-2=-3(-1)-5\\-2=3-5\\-2=-2\\[/tex]

we can see ordered pair [tex](1,8),(-2,1)and(-1,-2)[/tex] true for function [tex]y=-3x-5[/tex]

Answer:

640 cm²

Step-by-step explanation:

The ratio between the area two similar polygon are the ratio between their sides squared.

Given side S₁ and side S₂, you can find the area of the second shape by multiplying the area of the first shape by a factor of (S₂/S₁)².

This might sound confusing if you're not used to hearing math terms so lets solve it in this problem.

The side of the first trapezoid is 5cm, so S₁ = 5

The side of the second trapezoid is 20cm so S₂ = 20.

The ratio between them is 20/5=4

To find the area of the second shape, we just have to multiply the area of the first one by the ratio², ie. (S₂/S₁)².

40(4)² = 40(16) = 640 cm²

The sides are 7 inches and 5 inches. To get the perimeter, it's 7 +7 +5 + 5, which equals 24, and then 7 x 5 = 35 for the area.

Answer:

y=-2/3x+2

\\\\\\\\\\\\\\\\\\\\\

Answer: they lost 20 yards.

Step-by-step explanation

Answer:

A -20

Step-by-step explanation:

Answer:

The probability of selecting the given event = [tex]\frac{25}{52}[/tex]

Step-by-step explanation:

A card is drawn at random from a standard 52-card deck.

We have to find the probability of selecting an odd numbered card(3,5,7,9) or spade or both.For this we have to find the number of favourable cases.

Favorable cases = 13 (all the spades) + 12(4 odd numbered cards from each of the remaining 3 )

                         = 25

Final probability = [tex]\frac{number of favourable cases}{total number of cases}[/tex]

                             = [tex]\frac{25}{52}[/tex]

Hence the probability = [tex]\frac{25}{52}[/tex]

Answer:

968 ways

Step-by-step explanation:

This is a question of permutation and combination.

Each equation can have two different answers.

Thus the total number of cases will be (for 10 questions) :

[tex]2*2*2*2*.....10times=2^{10}[/tex] cases.

Now to find the number of ways to at least answer 3 questions False will be total minus the number of question with at most 2 False answers.

Total ways (at most 2 answers false) = [tex]1+10_C_1+10_C_2[/tex] ;

∴

The number of ways in which at least 3 have False as the answer is :

[tex]2^{10}-(1+10_C_1+10_C_2)\\=968[/tex] WAYS.

Answer:12

Step-by-step explanation:bcs in 1/3 it  has the same denominatoor

Answer:

The first picture is a function and the second picture is not.

Step-by-step explanation:

Reason - In the first picture, there is no repeating value of x. In other words, every x value has a y value. However, in the second picture, the x value, 2 goes to 2 and -3.

Using linear combination method, the solution to given system of equations are (-7, -15)

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated

Addition is used when the two equations have terms that are exact opposites, and subtraction is used when the two equations have terms that are the same.

Given system of equations are:

2x - y = 1  ---- eqn 1

3x - y = -6 ------ eqn 2

Subtract eqn 2 from eqn 1

2x - y = 1

3x - y = -6

(-) -------------

-x = 7

Substitute x = -7 in eqn 1

2(-7) - y = 1

-14 - y = 1

y = -14 - 1 = -15

Thus the solution to given system of equations are (-7, -15)

Answer:

[tex]time=1.2\times 10^{-1}\ second[/tex]

Step-by-step explanation:

Given:

The speed of the radio is [tex]3\times 10^{8}[/tex] meters per second.

The distance of the satellite from the earth is [tex]3.6\times 10^{7}[/tex] meter

The formula of the speed is

[tex]speed = \frac{distance}{time}[/tex]

For time the formula is.

[tex]time = \frac{distance}{speed}[/tex]

put distance and speed value in above equation.

[tex]time = \frac{3.6\times 10^{7}}{3\times 10^{8}}[/tex]

[tex]time = \frac{1.2 x 10^{7}}{10^{8}}[/tex]

[tex]time=1.2\times 10^{7}\times 10^{-8}[/tex]

[tex]time=1.2\times 10^{7-8}[/tex]

[tex]time=1.2\times 10^{-1}\ second[/tex]

Therefore, the radio will be take the time is [tex]1.2\times 10^{-1}\ second[/tex] or 0.12 seconds.

Answer: 14ft > 41/2

Step-by-step explanation:

Your answer is:

14ft > 41/2yd

I hope this helped! If so, please mark brainliest!

The question is incomplete. Here is the complete question:

The triangle will be rotated 180° clockwise around the point (3, 4) to create A A'B'C.Which

characteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select ALL that  apply.

(A) The coordinates of A'.

(B) The coordinates of B'.

(C) The perimeter of Δ A'B'C'.

(D) The area of Δ A'B'C'.

(E) The measure of ∠B'.

(F) The length of segment A'B'.

Answer:

(C) The perimeter of Δ A'B'C'.

(D) The area of Δ A'B'C'.

(E) The measure of ∠B'.

(F) The length of segment A'B'.

Step-by-step explanation:

Given:

A triangle ABC rotated by 180° clockwise around the vertex C(3,4) to create Δ A'B'C.

Now, a rotation is a rigid motion transformation. In rigid transformation, the  size, length, angle measures, perimeter and area of the figure doesn't change and remains the same as the original figure.

Rotation only changes the position of the points on the figure.

Here, as the triangle ABC is rotated about vertex C, the position of vertex A and B will change. But, the angles made by each of the vertices will remain same. Also, the side lengths of the triangle will remain the same. So, the perimeter and area will also not change. As the point of rotation is point C, the vertex C' will be same as vertex C.

So, the correct options are (C), (D), (E), and (F).